15.2.13 One dimensional random variables and their characteristics

Problem: The exchange rate of the US dollar against Euro can be described by the following function: \( \tau=\alpha \xi \), where \( \alpha \) is a parameter. The change in the Euro exchange rate is given by the following distribution table: \begin{tabular}{|c|c|c|c|c|c|c|} \hline\( x_{i} \) & 11,7 & 12 & 12,3 & 12,5 & 13 & 13,1 \\ \hline\( p_{i} \) & 0,1 & 0,1 & 0,2 & 0,15 & 0,2 & 0,25 \\ \hline \end{tabular} What will the distribution table of the random variable \( \tau \) be like? Find the expected value and the dispersion of \( \tau \).